Question: $\dfrac{ -9c - 7d }{ -7 } = \dfrac{ 8c + 5e }{ 5 }$ Solve for $c$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ -9c - 7d }{ -{7} } = \dfrac{ 8c + 5e }{ 5 }$ $-{7} \cdot \dfrac{ -9c - 7d }{ -{7} } = -{7} \cdot \dfrac{ 8c + 5e }{ 5 }$ $-9c - 7d = -{7} \cdot \dfrac { 8c + 5e }{ 5 }$ Multiply both sides by the right denominator. $-9c - 7d = -7 \cdot \dfrac{ 8c + 5e }{ {5} }$ ${5} \cdot \left( -9c - 7d \right) = {5} \cdot -7 \cdot \dfrac{ 8c + 5e }{ {5} }$ ${5} \cdot \left( -9c - 7d \right) = -7 \cdot \left( 8c + 5e \right)$ Distribute both sides ${5} \cdot \left( -9c - 7d \right) = -{7} \cdot \left( 8c + 5e \right)$ $-{45}c - {35}d = -{56}c - {35}e$ Combine $c$ terms on the left. $-{45c} - 35d = -{56c} - 35e$ ${11c} - 35d = -35e$ Move the $d$ term to the right. $11c - {35d} = -35e$ $11c = -35e + {35d}$ Isolate $c$ by dividing both sides by its coefficient. ${11}c = -35e + 35d$ $c = \dfrac{ -35e + 35d }{ {11} }$